Find the length of BC.
Give your answer to 1 decimal place.

Answer:

x = 3

Step-by-step explanation:

5x + 1 = 2x + 10

1.) Subtract 2x from both sides to get 2x on the other side

5x - 2x + 1 = 10

2.) Subtract 1 from both sides to get 1 to the other side

5x - 2x = 10 - 1

3.) Combine like terms

3x = 9

4.) Divide 3 on each side to get x by itself

x = 3

The total distance covered by the Ferris wheel after 6 rotations is 2616π feet

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The Ferris wheel has a radius of 218 feet. The total distance covered if the Ferris wheel makes one rotation is the perimeter of the wheel.

Perimeter = 2π * radius = 2π * 218 feet = 436π

For 6 rotations:

Total distance covered = 6 * 436π = 2616π

The total distance is 2616π feet

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The  function that models y in terms of x is y=0.804x

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=4.02-0/5-0

m=4.02/5 = 0.804

Now let us find y intercept

0=0.804(0)+b

b=0

Hence, the  function that models y in terms of x is y=0.804x

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For the given function,

Vertical asymptote = -5/4

Horizontal asymptote = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Range =  (-∞,-5/4) ∪ (-5/4,∞)

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The given function is

[tex]f(x) = \frac{-5x+2}{4x+5}[/tex]

The given function has a vertical asymptote at x = -5/4. This is because the function tends to ∞ as x tends to -5/4.

The horizontal asymptote of the function is when x tends to ∞ .

[tex]\lim_{x \to \infty} \frac{-5x+2}{4x+5} = \frac{-5+2/x}{4+5/x} = \frac{-5}{4}[/tex]

The horizontal asymptote of function is at y = -5/4.

Since at x = -5/4, the function becomes undefined.

The domain is all real numbers except x = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Since the function is not defined at y = -5/4 as well, the range is also

(-∞,-5/4) ∪ (-5/4,∞) .

Therefore for the given function,

Vertical asymptote = -5/4

Horizontal asymptote = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Range =  (-∞,-5/4) ∪ (-5/4,∞)

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Answer to question 1 is   [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex]

=========================================================

Explanation:

The first task is to find the equation of the line through the given points in the table.

Pick any two points you want. I'll pick (0,100) and (50,80)

Determine the slope:

[tex](x_1,y_1) = (0,100) \text{ and } (x_2,y_2) = (50,80)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{80 - 100}{50 - 0}\\\\m = \frac{-20}{50}\\\\m = -\frac{2}{5}\\\\[/tex]

The slope is -2/5.

The y intercept is b = 100 because of the point (0,100)

We go from [tex]\text{y} = m\text{x}+b[/tex] to [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]

Each point from the table is found on this line. For instance, let's check the point (140,44)

[tex]\text{y} = -\frac{2}{5}\text{x}+100\\\\44 = -\frac{2}{5}*140+100\\\\44 = -56+100\\\\44 = 44\\\\[/tex]

This confirms (140,44)

I'll let you check the other points.

------------------

Any point on the line mentioned represents a scenario where César spends all of the $50.

If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.

This means we want to shade the region below the boundary line [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]

We'll replace the equal sign with a "less than or equal" sign

We arrive at [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex] as the final answer to question 1.

Answer: Answer to question 1 is   =========================================================Explanation:The first task is to find the equation of the line through the given points in the table. Pick any two points you want. I'll pick (0,100) and (50,80) Determine the slope:The slope is -2/5.The y intercept is b = 100 because of the point (0,100)We go from  to Each point from the table is found on this line. For instance, let's check the point (140,44)This confirms (140,44)I'll let you check the other points.------------------Any point on the line mentioned represents a scenario where César spends all of the $50.If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.This means we want to shade the region below the boundary line We'll replace the equal sign with a "less than or equal" signWe arrive at  as the final answer to question 1.

Step-by-step explanation:

To get Desmos to show both square roots, you can use the formula y = √x + √(-x).  Desmos can then graph this equation, showing both the positive and negative square roots.

To get Desmos to show both square roots, you can use the formula y = √x + √(-x).This formula can be used to graph two square roots. The first square root is √x, which is the positive square root of x. The second square root is √(-x), which is the negative square root of x. To calculate the roots, you would take the square root of both x and -x. For example, if x is 4, the two roots would be √4 = 2 and √(-4) = 2i, where i is the imaginary unit. Desmos can then graph this equation, showing both the positive and negative square roots.

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The percent error of the measurement, to the nearest tenth of a percent, is 5.6.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

John measured a line to be 1.7 inches long.

The actual length of the line is 1.8 inches.

The amount of error = 1.8 - 1.7

The amount of error = 0.1

Let 1 - n be the required percentage of error.

Then applying the percentage formula,

1.8 x n /100 = 1.7

Applying cross multiplication,

we get,

1.8n = 170

n = 170/1.8

n = 94.4

So, 1 - n = 100 - 94.4 = 5.6

Therefore, the percentage is 5.6.

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The empirical rule states that in a normal distribution, 68% of the observations lie within 1 standard deviation from the mean, 95% of the observations lie within 2 standard deviations from the mean, and , 99.7% of the observations lie within 3 standard deviations from the mean.

a) -  Mean = U = 330 grams

standard deviation= [tex]\sigma=40 \: grams[/tex]

As per the empirical rule, 68% of the observations lie within 1 standard deviation from the mean.

Let [tex]X_1[/tex] and [tex]X_2[/tex] be the 2 random value, between which 68% of the observations lie.

Mathematically,

[tex]X1=U-\sigma[/tex]

[tex]X1[/tex] = 330 - 40

[tex]X1[/tex] =  290

Similarly,

[tex]X1=U-\sigma[/tex]

[tex]X1[/tex] = 330 + 40

[tex]X1[/tex] = 370

Thus, about 68 % of organs will be between 290 and 370 grams in weight.

b) - In this, we need to find the percentage of organs weighing between 250 grams and 410 grams.

We can rewrite 250 as follows:

250= 330− 80 ⇒ 30−2(40) ⇒ 330−2(σ)

The above value (250) lies within 2 standard deviations from the mean.

Similarly,

We can rewrite 410 as follows:

410 = 330+80 ⇒ 330+2(40) ⇒ 330+2(σ)

The above value (410) lies within 2 standard deviations from the mean.\

As per the empirical rule, 95% of the observations lie within 2 standard deviations from the mean.

Thus, 95% of organs weighs between 250 grams and 410 grams.

c)-As we have calculated in part(b) that 95% of the organs lie within 250 and 410 grams.

So, area outside these values = Total area under curve - 95%

= 100 - 95 ⇒ 5%

So, 5% of the area lies outside the 250 and 410 grams range.

From the property of normal curve, we know that the area under the curve is divided into 2 equal parts.So, we divide the area- 5% into 2 equal parts which gives 2.5%.

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The expressions 1/3(36m+12) and 12m+4  are equivalent

Equivalent expressions are defined as algebraic expressions that have the same solution but differ in the mode of the arrangement of values.

These expressions are known to have variables, constants, terms, coefficients, and factors.

They are also made up of mathematical operations.

We have the expression;

1/3(36m+12)

Now, expand the bracket

36m/3 + 12/3

Divide the values

12m + 4

Hence, the expression is 12m + 4

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Answer: x=-4, y=4

Step-by-step explanation:

We can use elimination method to solve this problem.

Let's eliminate y.

In equation 2, use the coefficient of y (i.e 5) to multiply equation 1. DO the same for other equation. Thus,

5(10x+7y=-12)

7(9x+5y=-16)

=> 50x+35y=-60

     63x+35y= -112

clearly, y can be eliminated by subtraction.

Therefore,

-13x = 52  [-63+50  and 112-60)]

x = -4.

When x = -4,

9x+5y =-16

9(-4) +5y =-16

5y = 36-16

y=4.

The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.

If the value of a numerical expression is terminating then they are the rational number then they are called a rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

Let's check all the options, then we have

A. √(4)² = 4, is a rational number.

B. √49 + √7 = 7 + √7, is an irrational number.

C. √225+ √169 = 25 + 13, is a rational number.

D. √2 x √121 = 11√2, is an irrational number.

E. √11 x 16 = 4√11, is an irrational number.

The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.

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Using the fact that the two triangles must be similar, we will see that d = 7.5 ft

To find the distance d we will use the fact that the two triangles must be similar triangles.

That means that the quotients between the legs must be equal.

For the triangle on the left side, the quotient is:

50ft/30ft

For the triangle on the right side, the quotient is:

d/height of the student.

We know that the height of the student is 4.5ft, so that quotient is:

d/4.5ft

Now we can write the equation:

d/4.5ft = 50ft/30ft

Solving this for d, we will get:

d = 4.5ft*(50ft/30ft) = 7.5 ft

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The sum of the distinct prime factors is (b) 14

From the question, we have the following parameters that can be used in our computation:

distinct prime factors of the number 560

The distinct prime factors of the number 560 are

Factors = 2, 5, 7.

When these numbers are added, we have

Sum = 2 + 5 + 7

Evaluate

Sum = 14

Hence , the sum is (b) 14

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Anwser : 23.8

Step 1: Subtract 5% from 25.

25 - (5% of 25) = 25 - (0.05 x 25)

Step 2: Simplify the equation.

25 - (0.05 x 25) = 25 - 1.25

Step 3: Subtract 1.25 from 25.

25 - 1.25 = 23.75

The terminal value formula helps estimate the value of a business beyond the explicit forecast period,

the terminal value formula = FCFF 6 / (WACC – Growth Rate)

We can say that in a DCF model with a five-year free cash flow projection, the terminal value formula = FCFF 6 / (WACC – Growth Rate)

It could be accountable that in finance, the terminal value (also known as “continuing value” or “horizon value” or "TV") of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. It is most likely often used in multi-stage discounted cash flow analysis and also allows for the limitation of cash flow projections to a several-year period; see Forecast period (finance). Forecasting results beyond such a period is impractical and exposes such projections to a variety of risks limiting their validity, primarily the great uncertainty involved in predicting industry and macroeconomic conditions beyond a few years.

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The value of the x in the given triangle is 7.5 units.

Proportion definition, comparative relation between things or magnitudes as to size, quantity, number.

Given is a triangle having sides, 12, 4 and 10 there is a missing side x we need to find is value,

Using the concept of parallel lines crest a proportion,

x / 10 = 12 / 16

x = 120 / 16

x = 7.5

Hence, the  value of the x in the given triangle is 7.5 units.

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In this equation, the value of x is fixed at 2, which means that every point on the graph will have the same x-coordinate value of 2. This creates a vertical line that passes through the point (2, y), where y can be any real number.

Therefore, the proper equation for the graph presented is:

[tex]x=2[/tex]

The required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4). which is the correct answer .

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

her, we have,

We have been given expression as:

3/4 x ( z^3 x 4)

To determine the equivalent expression to the given expression

3/4 x ( z^3 x 4)

⇒ 3* z^3

Here the variable z has an exponent is 3 which is positive,

Rearrange the terms of variables z  in the above expression

⇒3 · z³

Therefore, the required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4).

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The graph of the equation is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 3x

The above expression is a linear equation

A linear equation is represented as

y = mx + c

Where

Slope = m and y-intercept = c

This means that

y = 3x has a slope of 3 and a y-intercept of 0

Next, we plot the graph

See attachment for the graph of the equation

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The measure of angle C in radians is 3.6 radians.

The arc length of a circle is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.

Given that, the circle has a radius of 7 and angle C intercepts the arc with a length of 28π.

We know that, formula to find the arc length of circle is Arc length= θ/360 ×2πr

28π= θ/360×2π×7

4= θ/360×7

θ=1440/7

θ=205.7

θ=3.6 radians

Therefore, the measure of angle C in radians is 3.6 radians.

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The person with the largest container is Julie and the person with the smallest container is Jeff.

The volume of each container has to be determined.

Volume of a cylinder = πr²h

Where:

Volume of Ms. Liu's container:

3.14 x 3² x 12 = 339.12 in³

Volume of Ms. Julie's container:

Volume = 3.14 x 3² x 24 = 678.24 in³

Volume of Jeff's container:

Volume = 3.14 x 1² x 24 = 75.36 in³

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The completed two-column table used to prove that the quadrilateral WXYZ is a parallelogram is presented as follows;

Statement     [tex]{}[/tex]                                              Reason

1. m∠y = 49, m∠z = 131°, m∠w = 49  [tex]{}[/tex]       Given

2. m∠y + m∠z + m∠w + m∠x = 360 [tex]{}[/tex]    1. ∠ sum property of a quadrilateral

3. 49 + 131 + 49 + m∠x = 360[tex]{}[/tex]                Substitution Property of Equality

4. 229 + m∠x = 360   [tex]{}[/tex]                           2. Summation of values

5. m∠x = 131                                           3. Subtraction Property of Equality

6. ∠x ≅ ∠z and ∠w ≅ ∠y [tex]{}[/tex]                     Angles with equal measures are ≅

7. WXYZ is a parallelogram                 4. The opposite ∠s of a ║ are ≅

A parallelogram is a quadrilateral that has two pairs of parallel facing sides.

The details of the reasons used in the two-column table method to prove that the quadrilateral WXYZ is  parallelogram are illustrated as follows;

∠ sum property of a quadrilateral

The angle (∠) sum property of a quadrilateral, indicates that the addition of the four interior angles of a quadrilateral has a result of 360°

Summation of a set of values

The sum of the values 49 + 131 + 49 is 229

Subtraction Property of Equality

The subtraction property of equality states that the subtraction of the same amount from both sides of an equation produces two new quantities or expressions on both sides of the equation that remain equivalent.

Angles with the same measures are ≅

Angles that are congruent, ≅, are angles that have the same measure

The opposite angles of a ║ are ≅

The angles located in the facing corners of a parallelogram, ║, are congruent.

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Answer:

8 cm

Step-by-step explanation:

15 - 7 = 8

The length of the right side equals the length of the left side.  The left side has a length of 15 and the part that we know for the right side is 7.

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

=  5 /100  * 78 =  39 /10  = 3.9

$3.90

The numeric values for each of the expressions are given as follows:

1. 9.8t² + 20t + 8:

2. -3(2.1x - 7.9):

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Then the numeric values are given as follows:

1. 9.8t² + 20t + 8:

2. -3(2.1x - 7.9):

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a. Here's a table of values for the number of rounds and the number of teams participating:

Round Number of Teams

1             16

2              8

3                  4

4             2

5       1 (Champion)

.b. domain: [1 5]

Range: {1 16]

C. Rate of decay = 8

D. Decay factor = 0.5

b. The reasonable domain of this function would be the number of rounds, and the range would be the number of teams participating in each round.

The domain would be all positive integers from 1 to the maximum number of rounds,

The range would be all positive integers from 1 to the starting number of teams (16 in this case).

c. To find the rate of decay, we can calculate the ratio of the change in the number of teams to the change in the number of rounds.

Using Round 1 to Round 2,

= (16 - 8) / (2 - 1)

= 8.

d. The decay factor is the ratio of the number of teams in a given round to the number of teams in the previous round.

Using Round 1 to Round 2, the decay factor is

= 8 / 16

= 0.5

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There will be 360 different ways without using the same airline or shipping line.

A combination in mathematics is a selection of items from a set with distinct members, where the order of selection is irrelevant.

Let's first consider the number of ways the man can choose his outbound journey. He has 6 airlines to choose from, and once he has made his choice of airline, he has 4 shipping lines to choose from.

Therefore, there are 6 × 4 = 24 ways he can choose his outbound journey.

For his return journey, he cannot use the same airline or shipping line that he used for his outbound journey.

This means he now has 5 airlines and 3 shipping lines to choose from. Therefore, there are 5 × 3 = 15 ways he can choose his return journey.

The total number of ways he can make his journey is:

24 × 15 = 360

Therefore, he can make his journey in 360 different ways without using the same airline or shipping line.

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